Project Euler is an ever-expanding collection of computational problems (i.e. problems that involve mathematical thinking but are too hefty to be done by hand). As of yesterday, it contained 355 problems. Some of them seem boring, but each is a challenge, and a good way of learning programming. There many sites discussing solutions, and lots of opportunities to cheat, but then you miss on the pleasure of actually nailing a problem. Quite a lot are number theoretic, but you can find anything from cryptography to networks to pizza toppings to testing sheep for a rare virus. Many involve the art of counting, i.e. combinatorics, an art that comes in handy in field after field. Opportunity to hone your R or MAPLE skills, though I would recommend using the problems to learn another language, say Python.
For some history of the project and its progenitor, Colin Hughes, see this article in The Atlantic. The best advice seems to be the generic one: start at the beginning…
Lollipop to anyone who does all the problems, or indeed number 155.